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I have made 9 models using simple linear regression. I'm now checking that each of models meets the assumption of homogeneity of variance. Each of the models used either categorical or numeric (year as an integer) IVs. I carried out a Levenes test either at each level of a categorical IV or against the integer IV (year).

I have concluded that the IVs for which the p>0.05 show homogenous variance, while IVs for which the p<0.05 show heterogenous variance. Three (out of 9) models contained IVs for which the p<0.05. These were Model (1 out of 2 IVs showed p<0.05), Model 2 (2 out of 2 IVs showed p<0.05) and Model 3 (3 out of 3 IVs showed p<0.05).

The following plots show these 3 models (IVs which have p<0.05 only):

Model 1

Model 2

Model 3

My questions are:

• am I correct in concluding that the Levenes tests which gave a p<0.05 indicates a violation of homogeneity of variance?

• in Model 1, in which only 1 out of 2 IVs gave a p<0.05, need only the IV for which p<0.05 be corrected (as opposed to also correcting the IV for which p>0.05)?

• looking at the plots, could anyone suggest possible solutions for the IVs which gave p>0.05: transformation of response variable, interaction IVs, quadratic IVs, Poisson generalised linear model, generalised additive modelling?????

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